A nonparametric classification procedure based on distribution-free tolerance regions is presented. Without knlowledge of the class probability distributions, the procedure gives information about the expected performance of the classifier through use of only one sample of statistically independent observations from each class. With this procedure, a two-class discriminant can be designed for a given expected false alarm probability or for a given confidence that the false alarm probability is less than a given amount. Three ordering methods are presented that appear intuitively reasonable for minimizing the miss probability. Even though the methods do not, in general, meet this objective, they are easily implemented on a computer and can give good results. A procedure for obtaining a measure of the miss probability is also presented. These methods are applied to the problem of verifying the purported identity of a speaker from a sample of the speaker's voice.